In this paper, we have discussed root subspace decomposition of linear space, and for the linear space have decomposed direct sum of root subspace, a primary proof is given.

文章讨论了线性空间的根子空间分解，并对线性空间分解成根子空间的直和给出了较为初等的证明。

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The direct sum decomposition of the addition of a linear transformation under the coprime polynomial was given, and it was used in the proof of some equality about the rank of idempotent matrix.

给出了两两互素多项式下线性变换的核的直和分解，并应用于幂等矩阵（对合矩阵）的秩的等式证明中。

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